Series expansion for a stochastic sandpile

Details Series expansion for a stochastic sandpile Series expansion for a stochastic sandpile

2003-06-09

arxiv.org/abs/cond-mat/0306214v2

Physics

Condensed Matter

Statistical Mechanics

Extended series and improved analysis

Scientific paper

10.1088/0305-4470/37/4/004

Using operator algebra, we extend the series for the activity density in a one-dimensional stochastic sandpile with fixed particle density p, the first terms of which were obtained via perturbation theory [R. Dickman and R. Vidigal, J. Phys. A35, 7269 (2002)]. The expansion is in powers of the time; the coefficients are polynomials in p. We devise an algorithm for evaluating expectations of operator products and extend the series to O(t^{16}). Constructing Pade approximants to a suitably transformed series, we obtain predictions for the activity that compare well against simulations, in the supercritical regime.

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